2017 AIME II Problems/Problem 15: Difference between revisions
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==Problem== | |||
Tetrahedron <math>ABCD</math> has <math>AD=BC=28</math>, <math>AC=BD=44</math>, and <math>AB=CD=52</math>. For any point <math>X</math> in space, define <math>f(X)=AX+BX+CX+DX</math>. The least possible value of <math>f(X)</math> can be expressed as <math>m\sqrt{n}</math>, where <math>m</math> and <math>n</math> are positive integers, and <math>n</math> is not divisible by the square of any prime. Find <math>m+n</math>. | Tetrahedron <math>ABCD</math> has <math>AD=BC=28</math>, <math>AC=BD=44</math>, and <math>AB=CD=52</math>. For any point <math>X</math> in space, define <math>f(X)=AX+BX+CX+DX</math>. The least possible value of <math>f(X)</math> can be expressed as <math>m\sqrt{n}</math>, where <math>m</math> and <math>n</math> are positive integers, and <math>n</math> is not divisible by the square of any prime. Find <math>m+n</math>. | ||
==Solution== | |||
=See Also= | |||
{{AIME box|year=2017|n=II|num-b=14|num-a=16}} | |||
{{MAA Notice}} | |||
Revision as of 12:02, 23 March 2017
Problem
Tetrahedron 
has 
, 
, and 
. For any point 
in space, define 
. The least possible value of 
can be expressed as 
, where 
and 
are positive integers, and is not divisible by the square of any prime. Find 
.
Solution
See Also
| 2017 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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